Skip to main content
Log in

On Multivariate Polynomials and Construction of Covariant Bounded Current Vectors

  • Published:
Moscow University Physics Bulletin Aims and scope

Abstract

Equations related to the sums of the products of multivariate polynomials are studied. One set of polynomials is considered as determined and the other is sought. In the general case of defining polynomials, a series of relationships is obtained for the degrees of polynomials and determinants of matrices composed of polynomial coefficients. On the basis of these relationships and the continuity equation, a number of variants of covariant vectors of limited current density are presented. The results can definitely be considered correct if the accelerations are not too large. The case where the current vector depends on the variable whose value at transition to the stationary state is dictated by the conditions under which such a transition is treated (if these conditions are unknown, then particular elements of uncertainty are possible in the stationary states).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. M. Marckus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities (Allyn and Bacon, Boston, 1964).

    Google Scholar 

  2. I. V. Proskuryakov and A. P. Mishina, Higher Algebra. Linear Algebra, Polynomials, General Algebra (Fizmatgiz, Moscow, 1962; Pergamon, Oxford, New York, Paris, 1965).

  3. V. A. Il’in and E. G. Poznyak, Linear Algebra (Nauka, Fizmatlit, Moscow, 1999).

  4. V. B. Berestetskii, E. M. Lifshitz, and A. P. Pitaevskii, Course of Theoretical Physics, Vol. 4: Quantum Electrodynamics (Nauka, Moscow, 1980; Pergamon, Oxford, 1982).

  5. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 2: The Classical Theory of Fields (Pergamon, Oxford, 1975; Nauka, Moscow, 1988).

  6. M. B. Ependiev, Mosc. Univ. Phys. Bull. 69, 474 (2014).

    Article  ADS  Google Scholar 

  7. M. B. Ependiev, J. Mod. Phys. 5, 601 (2015).

    Article  Google Scholar 

  8. J. S. Nodvik, Ann. Phys. 28, 225 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  9. H. Spohn, arXiv: math-ph/9908024v1 (1999).

  10. D. Bohm, Quantum Theory (Dover, New York, 1989).

    MATH  Google Scholar 

  11. A. A. Sokolov, I. M. Ternov, and V. Ch. Zhukovskii, Quantum Mechanics (Nauka, Moscow, 1979; Mir, Moscow, 1984).

  12. M. B. Ependiev, Theoretical Foundations of Physics, 2nd ed. (IKI, Moscow, Izhevsk, 2018) [in Russian].

    Google Scholar 

Download references

ACKNOWLEDGMENTS

The author thanks A.V. Borisov for his scientific advice and aid in the work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. B. Ependiev.

Additional information

Translated by E. Oborin

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ependiev, M.B. On Multivariate Polynomials and Construction of Covariant Bounded Current Vectors. Moscow Univ. Phys. 75, 309–315 (2020). https://doi.org/10.3103/S0027134920040074

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027134920040074

Keywords:

Navigation